Question 1209839
<br>
Given:<br>
{{{log(8,3)=P}}}
{{{log(3,5)=Q}}}<br>
To find:<br>
{{{log(15,72)}}}<br>
{{{log(15,72)=log(b,72)/log(b,15)}}}
{{{log(b,72)=log(b,8)+log(b,9)}}}<br>
{{{log(b,15)=log(b,3)+log(b,5)}}}
{{{log(15,72)=(log(b,8)+log(b,9))/(log(b,3)+log(b,5))}}}<br>
With the given information, we want to use base 3 logarithms.<br>
{{{log(8,3)=P}}} --> {{{log(3,8)=1/P}}}<br>
{{{log(15,72)=(log(3,8)+log(3,9))/(log(3,3)+log(3,5))=((1/P)+2)/(1+Q)}}}<br>
The result can be written in many different forms....<br>
ANSWER: {{{((1/P)+2)/(1+Q)}}}<br>